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A mathematical study of the linear theory for orthotropic elastic simple shells
Author(s) -
Bîrsan Mircea,
Altenbach Holm
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1253
Subject(s) - orthotropic material , uniqueness , simple (philosophy) , mathematics , mathematical analysis , surface (topology) , point (geometry) , geometry , finite element method , physics , thermodynamics , philosophy , epistemology
The theory of simple shells is a surface‐related Cosserat model for thin elastic shells. In this direct approach, each material point is connected with a triad of rigidly rotating directors. This paper presents a study of the governing equations for orthotropic elastic simple shells in the framework of the linearized theory. We establish the uniqueness of classical solutions, without any restrictive assumption on the strain energy function. The continuous dependence of solutions on the body loads and initial data is proved. Also, the existence of weak solutions to the equations of simple shells is proved by means of an inequality of Korn's type established for such directed surfaces. Copyright © 2009 John Wiley & Sons, Ltd.